Joint Modeling of Floor Elevations and Thickness of a Bauxite Unit Considering Trend, Histogram and Variogram Uncertainty

Laterite-type bauxite deposits typically exhibit a highly irregular boundary between the bauxite and underlying ferricrete units. This irregularity cannot be accurately modeled using data collected from sparsely spaced drillholes (e.g., 76.2×76.2 m or 250×250 ft). Geological models that assume a sharp and nearly horizontal bauxite/ferricrete contact can result in significant errors when calculating the in situ bauxite resource (in volume) and in misclassifying ore and waste during mining operations. Two primary sources of uncertainty must be addressed when modeling lateritic bauxite deposits: (1) grade uncertainty associated with variations in Al2O3 and SiO2% concentrations, and (2) geometric uncertainty related to lateral variations in the bauxite/ferricrete contact. Among these, geometric uncertainty is more critical, as accurately estimating bauxite ore tonnage depends on the precise modeling of the lateral variation in the boundary between the bauxite and underlying ferricrete units. This study evaluates the uncertainty of the bauxite resource within a selected mine area in northern Queensland, Australia, particularly in cases where experimental data are sparse and limited. To address this, the position variable (bauxite floor elevations) and the thickness of the bauxite unit are jointly simulated under two scenarios. In the first scenario, the histograms, variogram model parameters, and the estimated trend of the variables of interest are assumed to be known with certainty; that is, parameter uncertainty is not considered in the modeling process. In the second scenario, the histograms, variogram model parameters, and the estimated trend are considered uncertain, and parameter uncertainty is explicitly incorporated into the modeling process using the multivariate spatial bootstrap procedure. The methodology is applied to both scenarios, showing that incorporating parameter uncertainty in geostatistical modeling results in greater dispersion of the uncertainty associated with the in situ bauxite resource. The results show that the 95% confidence intervals for the in situ bauxite ore volume, derived from bauxite thickness realizations, vary depending on whether parameter uncertainty is considered. When parameter uncertainty is incorporated, the interval is (390,123 m3 and 393,223 m3), whereas without parameter uncertainty, it is (382,332 m3 and 384,373 m3). This comparison highlights that incorporating parameter uncertainty provides a more realistic assessment of resource risk in the modeling process.